Geodesic
Cabling procedure for the colored HOMFLY polynomials
Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 1, pp. 3-68 Cet article a éte moissonné depuis la source Math-Net.Ru

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We discuss using the cabling procedure to calculate colored HOMFLY polynomials. We describe how it can be used and how the projectors and $\mathcal R$-matrices needed for this procedure can be found. The constructed matrix expressions for the projectors and $\mathcal R$-matrices in the fundamental representation allow calculating the HOMFLY polynomial in an arbitrary representation for an arbitrary knot. The computational algorithm can be used for the knots and links with $|Q|m\le12$, where $m$ is the number of strands in a braid representation of the knot and $|Q|$ is the number of boxes in the Young diagram of the representation. We also discuss the justification of the cabling procedure from the group theory standpoint, deriving expressions for the fundamental $\mathcal R$-matrices and clarifying some conjectures formulated in previous papers.
Keywords: Chern–Simons theory, knot theory, representation theory. 
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A. S. Anokhina; A. A. Morozov. Cabling procedure for the colored HOMFLY polynomials. Teoretičeskaâ i matematičeskaâ fizika, Tome 178 (2014) no. 1, pp. 3-68. http://geodesic.mathdoc.fr/item/TMF_2014_178_1_a0/

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